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Freeform surface model conversion: from Zernike Standard Sag to Extended Polynomial

  • July 13, 2023
  • 1 reply
  • 420 views

Igor

Hi everyone!

I am looking for the quickest and most efficient way of converting the surface data in Zernike Standard Sag form to Extended Polynomial. Any help is appreciated!

Regards.

Best answer by Erin.Elliott

Hi, Igor.  The easiest way would be to generate a sag map for the surface, go to the Text view, save the data.  Then read it into Matlab or Mathematica or the like, and fit the Extended Polynomial terms to the data to generate the coefficient values needed for the Extended Polynomial.  If you have the coefficients in Excel, you can copy and paste into the LDE of OpticStudio; there’s no need to type all the values or paste them one-by-one.  You could also easily write a quick ZPL macro that could read and write the values in for you.

You can also do this conversion exactly, by writing out the full surface shape and matching terms to find the analytic conversion between the Zernike Standard polynomials and those of the Extended Polynomial.  That’s more work, because you have to pay attention to the coefficient definitions, but it can be quite useful to have lying around. 

I just published an article on converting the Zernikes into Cartesian form:

Erin

1 reply

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  • Zemax Staff
  • 53 replies
  • Answer
  • December 13, 2023

Hi, Igor.  The easiest way would be to generate a sag map for the surface, go to the Text view, save the data.  Then read it into Matlab or Mathematica or the like, and fit the Extended Polynomial terms to the data to generate the coefficient values needed for the Extended Polynomial.  If you have the coefficients in Excel, you can copy and paste into the LDE of OpticStudio; there’s no need to type all the values or paste them one-by-one.  You could also easily write a quick ZPL macro that could read and write the values in for you.

You can also do this conversion exactly, by writing out the full surface shape and matching terms to find the analytic conversion between the Zernike Standard polynomials and those of the Extended Polynomial.  That’s more work, because you have to pay attention to the coefficient definitions, but it can be quite useful to have lying around. 

I just published an article on converting the Zernikes into Cartesian form:

Erin